Tire wear and pressure. Suppose you want to use the coding system for observational data to fit a second-order model to the tire pressureÃ¢â¬âautomobile mileage data in Exercise 10, which are repeated in the table.
(a) Give the equation relating the coded variable u to pressure, x, using the coding system for observational data.
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(b) Calculate the coded values, u.
(c) Calculate the coefficient of correlation r between the variables x and x2.
(d) Calculate the coefficient of correlation r between the variables u and u2. Compare this value to the value computed in part c.
(e) Fit the model
E(y) = ÃÂ²0 + ÃÂ²1u + ÃÂ²2u2 using available statistical software. Interpret the results.